Recently observed microwave resonances in the spectrum of a two-dimensional electon gas under high magnetic fields in the neighborhood of the fractional filling ν = 1/3 were interpreted as signatures of a weakly pinned Wigner solid. Using the rotating-and-vibrating electron-molecule (RVEM) theory [Yannouleas and Landman, Phys. Rev. B 66, 115315 (2002); Phys. Rev. A 81, 023609 (2010)], in conjun...

Fourier quasicrystals are tempered distributions μ which satisfy symmetric conditions on and μˆ. This suggests that techniques from time-frequency analysis could possibly be useful tools in the study of such structures. In this paper we explore direction considering type representations instead separately distribution its transform. More precisely prove a Rd whose Wigner transform, W(μ), is sup...

We derive the kinetic equations for both the covariant and equal-time Wigner functions of Dirac particles with electromagnetic, scalar and pseudoscalar interactions. We emphasize the constraint equations for the spinor components in the equal-time formulation. PACS: 03.65.Bz, 05.60.+w, 52.60.+h. Typeset using REVTEX 1 One of the recent progresses in transport theory [1,2] is the establishment o...

In this paper we use the Wigner transform to study properties of solutions to the Schrödinger equation. In particular, we present an elementary proof of the time decay inequalities for the free particle and harmonic oscillator. Furthermore, we estimate certain localized integral quantities in phase space, involving the Wigner transform of solutions to the Schrödinger equation.

We show that quasiholes persist near the edge of incompressible Quantum Hall state forming a Wigner structure. The average density of quasiholes is fixed by electrostatics and decreases slowly with increasing distance from the edge. As we see from elementary reasoning, their specific arrangement can not be a regular Wigner lattice and shows a complex hierarchical structure of

We show that, for sequences of vectors of multiple Wigner integrals with respect to a free Brownian motion, componentwise convergence to semicircular is equivalent to joint convergence. This result extends to the free probability setting some findings by Peccati and Tudor (2005), and represents a multidimensional counterpart of a limit theorem inside the free Wigner chaos established by Kemp, N...